There are coffee machines which contain a brewing apparatus into which one or more portion packs with coffee can be introduced. For this purpose, the brewing chamber has a holder which can be removed from the coffee machine in order for a corresponding portion pack to be introduced. The portion pack is then introduced into the brewing apparatus and a cover, which seals a brewing chamber via a sealing ring, is closed. The disadvantage with this type of sealing is that the sealing ring is subject to a relatively high level of wear and, in addition, a contact pressure of the sealing ring is only achieved via the mechanical means of the housing. After a period of time, leakages may thus occur and the sealing ring has to be exchanged. Furthermore, such a design only allows a relatively high pressure to build up in the brewing chamber to a limited extent. Finally, there is also the disadvantage that, during the coffee-brewing operation, the coffee powder collapses to some extent and the fluid introduced into the brewing chamber can thus flow past the portion pack through gaps formed (bypass effect) without any extraction taking place.